x^2-48x+9=0

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Solution for x^2-48x+9=0 equation: 


Simplifying
x2 + -48x + 9 = 0

Reorder the terms:
9 + -48x + x2 = 0

Solving
9 + -48x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -48x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -48x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -48x + x2 = 0 + -9
-48x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-48x + x2 = -9

The x term is -48x.  Take half its coefficient (-24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
-48x + 576 + x2 = -9 + 576

Reorder the terms:
576 + -48x + x2 = -9 + 576

Combine like terms: -9 + 576 = 567
576 + -48x + x2 = 567

Factor a perfect square on the left side:
(x + -24)(x + -24) = 567

Calculate the square root of the right side: 23.8117618

Break this problem into two subproblems by setting 
(x + -24) equal to 23.8117618 and -23.8117618.


Subproblem 1
x + -24 = 23.8117618

Simplifying
x + -24 = 23.8117618

Reorder the terms:
-24 + x = 23.8117618

Solving
-24 + x = 23.8117618

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '24' to each side of the equation.
-24 + 24 + x = 23.8117618 + 24

Combine like terms: -24 + 24 = 0
0 + x = 23.8117618 + 24
x = 23.8117618 + 24

Combine like terms: 23.8117618 + 24 = 47.8117618
x = 47.8117618

Simplifying
x = 47.8117618


Subproblem 2
x + -24 = -23.8117618

Simplifying
x + -24 = -23.8117618

Reorder the terms:
-24 + x = -23.8117618

Solving
-24 + x = -23.8117618

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '24' to each side of the equation.
-24 + 24 + x = -23.8117618 + 24

Combine like terms: -24 + 24 = 0
0 + x = -23.8117618 + 24
x = -23.8117618 + 24

Combine like terms: -23.8117618 + 24 = 0.1882382
x = 0.1882382

Simplifying
x = 0.1882382


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {47.8117618, 0.1882382}

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